<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">G</font> be  <a href="group_1.html#V1">strict</a> <a href="gr_cy_1.html#V1">cyclic</a> <a href="group_1.html#NM1">Group</a>;<br/>

<b>assume </b><a NAME="E1:28"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">G</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="group_2.html#K5">(1).</a> <font color="Maroon">G</font>
 ;<br/>

<b>let </b><font color="Maroon">H</font> be  <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G</font>;<br/>

<b>assume </b><a NAME="E2:28"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">H</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="group_2.html#K5">(1).</a> <font color="Maroon">G</font>
 ;<br/>

<b>consider </b><font color="Maroon">b</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font><b> such that </b><br/><a NAME="E4:28"/><i><font color="Green">E41</font></i>: 
 <a href="group_1.html#G1">HGrStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font>,the <a href="group_1.html#U1">mult</a> of <font color="Maroon">G</font> #) <a href="hidden.html#R1">=</a>  <a href="group_4.html#K5">gr</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">b</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="gr_cy_1.html#D9">GR_CY_1:def 9</a></i>;<br/>
<b>consider </b><font color="Maroon">i</font> being   <a href="int_1.html#NM1">Integer</a>;<br/>
<a NAME="E6:28"/>
 ex <font color="Olive">m</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">m</font> &amp; <font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Olive">m</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H</font> &amp; ( for <font color="Olive">j</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">j</font> &amp; <font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Olive">j</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H</font> holds <br/><font color="Olive">m</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">j</font> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1"><b>proof </b></a><div class="add">

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ] <b>means </b>( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">a<sub>1</sub></font> &amp; <font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">a<sub>1</sub></font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H</font> );<br/>
<a NAME="E1:28_1"/><i><font color="Green">E42</font></i>: 
 ex <font color="Olive">k</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">k</font>]
 
<b>by </b><i>, , , </i>;<br/>
<a NAME="E2:28_1"/>
 ex <font color="Olive">m</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">m</font>] &amp; ( for <font color="Olive">j</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">j</font>] holds <br/><font color="Olive">m</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">j</font> ) )
 
<b>from </b><i><a class="ref" href="nat_1.html#S5">NAT_1:sch 5</a>();<br/></i>
<b>hence </b><a NAME="E3:28_1"/>
 ex <font color="Olive">m</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">m</font> &amp; <font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Olive">m</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H</font> &amp; ( for <font color="Olive">j</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">j</font> &amp; <font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Olive">j</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H</font> holds <br/><font color="Olive">m</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">j</font> ) )
 ;<br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon">m</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E8:28"/><i><font color="Green">E47</font></i>: 
( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m</font> &amp; <font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">m</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H</font> &amp; ( for <font color="Olive">j</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">j</font> &amp; <font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Olive">j</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H</font> holds <br/><font color="Maroon">m</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">j</font> ) )
 ;<br/>
<b>set </b><font color="Maroon">c</font> = <font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">m</font>;<br/>
<b>reconsider </b><font color="Maroon">c</font> = <font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">m</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">H</font> <b>by </b><i>, <a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>
<a NAME="E10:28"/><i><font color="Green">E48</font></i>: 
for <font color="Olive">a</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">H</font>  ex <font color="Olive">i</font> being  <a href="int_1.html#NM1">Integer</a> st <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> <a href="group_1.html#K6">|^</a> <font color="Olive">i</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">H</font>;<br/>

<a NAME="E1:28_2"/>
 ex <font color="Olive">t</font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( <font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Olive">t</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H</font> &amp; <font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Olive">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:28_2_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">a</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">G</font>
 
<b>by </b><i><a class="ref" href="group_2.html#T50">GROUP_2:50</a></i>;<br/>
<a NAME="E2:28_2_1"/><b>then </b><i><font color="Green">E63</font></i>: 
<font color="Maroon">a</font> <a href="rlvect_1.html#R1">in</a>  <a href="group_4.html#K5">gr</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">b</font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E3:28_2_1"/>
<font color="Maroon">a</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>
 
<b>by </b><i>, <a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>
<a NAME="E4:28_2_1"/><b>then </b>
 ex <font color="Olive">j1</font> being  <a href="int_1.html#NM1">Integer</a> st <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Olive">j1</font>
 
<b>by </b><i>, <a class="ref" href="gr_cy_1.html#T25">GR_CY_1:25</a></i>;<br/>
<b>then consider </b><font color="Maroon">j1</font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E6:28_2_1"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">j1</font>
 ;<br/>
<a NAME="E7:28_2_1"/>
<font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">j1</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H</font>
 
<b>by </b><i>, <a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E8:28_2_1"/>
 ex <font color="Olive">t</font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( <font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Olive">t</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H</font> &amp; <font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Olive">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> )
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon">t</font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:28_2"/><i><font color="Green">E65</font></i>: 
( <font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">t</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H</font> &amp; <font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> )
 ;<br/>
<a NAME="E4:28_2"/>
 ex <font color="Olive">r</font>, <font color="Olive">s</font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">s</font> &amp; <font color="Olive">s</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m</font> &amp; <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="xcmplx_0.html#K3">*</a> <font color="Olive">r</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Olive">s</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_2_2"><b>proof </b></a><div class="add">

<b>take </b><font color="Maroon">r</font> = <font color="Maroon">t</font> <a href="int_1.html#K5">div</a> <font color="Maroon">m</font>;<br/>

<b>take </b><font color="Maroon">s</font> = <font color="Maroon">t</font> <a href="int_1.html#K6">mod</a> <font color="Maroon">m</font>;<br/>

<a NAME="E1:28_2_2"/><i><font color="Green">E68</font></i>: 
<font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">m</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">s</font>
 
<b>by </b><i>, <a class="ref" href="newton.html#T80">NEWTON:80</a></i>;<br/>
<a NAME="E2:28_2_2"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">t</font> <a href="int_1.html#K6">mod</a> <font color="Maroon">m</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="ref" href="newton.html#T78">NEWTON:78</a></i>;<br/>
<a NAME="E3:28_2_2"/>
<font color="Maroon">t</font> <a href="int_1.html#K6">mod</a> <font color="Maroon">m</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m</font>
 
<b>by </b><i>, <a class="ref" href="newton.html#T79">NEWTON:79</a></i>;<br/>
<b>hence </b><a NAME="E4:28_2_2"/>
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">s</font> &amp; <font color="Maroon">s</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m</font> &amp; <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">r</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">s</font> )
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon">r</font> being   <a href="int_1.html#NM1">Integer</a>, <font color="Maroon">s</font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E6:28_2"/><i><font color="Green">E71</font></i>: 
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">s</font> &amp; <font color="Maroon">s</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m</font> &amp; <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">r</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">s</font> )
 ;<br/>
<b>reconsider </b><font color="Maroon">s</font> = <font color="Maroon">s</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i>, <a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/>
<i><font color="Green">E72</font></i>: <font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">t</font> = 
<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">r</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">s</font></span>)</span>
<b>by </b><i>, <a class="ref" href="group_1.html#T63">GROUP_1:63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">m</font></span>)</span> <a href="group_1.html#K6">|^</a> <font color="Maroon">r</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">s</font></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#T67">GROUP_1:67</a></i>
;<br/>
<a NAME="E9:28_2"/><i><font color="Green">E73</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">m</font></span>)</span> <a href="group_1.html#K6">|^</a> <font color="Maroon">r</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E10:28_2"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">s</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_2_4"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon">u</font> = <font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">t</font>;<br/>
<b>set </b><font color="Maroon">v</font> = <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">m</font></span>)</span> <a href="group_1.html#K6">|^</a> <font color="Maroon">r</font>;<br/>
<a NAME="E1:28_2_4"/><i><font color="Green">E75</font></i>: 
( <font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">m</font></span>)</span> <a href="group_1.html#K6">|^</a> <font color="Maroon">r</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">s</font></span>)</span> &amp; <font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">t</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">m</font></span>)</span> <a href="group_1.html#K6">|^</a> <font color="Maroon">r</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H</font> )
 
<b>by </b><i>, , </i>;<br/>
<b>then </b><i><font color="Green">E76</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">m</font></span>)</span> <a href="group_1.html#K6">|^</a> <font color="Maroon">r</font></span>)</span> <a href="group_1.html#K3">"</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">t</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">m</font></span>)</span> <a href="group_1.html#K6">|^</a> <font color="Maroon">r</font></span>)</span> <a href="group_1.html#K3">"</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">m</font></span>)</span> <a href="group_1.html#K6">|^</a> <font color="Maroon">r</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">s</font></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">G</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">s</font></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D6">GROUP_1:def 6</a></i>
<br/>.= 
<font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">s</font>
<b>by </b><i><a class="ref" href="group_1.html#D5">GROUP_1:def 5</a></i>
;<br/>
<a NAME="E3:28_2_4"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">m</font></span>)</span> <a href="group_1.html#K6">|^</a> <font color="Maroon">r</font></span>)</span> <a href="group_1.html#K3">"</a>  <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H</font>
 
<b>by </b><i>, <a class="ref" href="group_2.html#T60">GROUP_2:60</a></i>;<br/>
<b>hence </b><a NAME="E4:28_2_4"/>
<font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">s</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H</font>
 <b>by </b><i>, , <a class="ref" href="group_2.html#T59">GROUP_2:59</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E11:28_2"/>
<font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">G</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_2_5"><b>proof </b></a><div class="add">

<a NAME="E1:28_2_5"/>
<font color="Maroon">s</font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E2:28_2_5"/>
<font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="group_1.html#T43">GROUP_1:43</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E12:28_2"/><b>then </b>
<font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">m</font></span>)</span> <a href="group_1.html#K6">|^</a> <font color="Maroon">r</font>
 
<b>by </b><i>, <a class="ref" href="group_1.html#D5">GROUP_1:def 5</a></i>;<br/>
<a NAME="E13:28_2"/><b>then </b><i><font color="Green">E77</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">m</font></span>)</span> <a href="group_1.html#K6">|^</a> <font color="Maroon">r</font>
 
<b>by </b><i/>;<br/>
<a NAME="E14:28_2"/>
<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">m</font></span>)</span> <a href="group_1.html#K6">|^</a> <font color="Maroon">r</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">r</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E15:28_2"/>
 ex <font color="Olive">i</font> being  <a href="int_1.html#NM1">Integer</a> st <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> <a href="group_1.html#K6">|^</a> <font color="Olive">i</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<a NAME="E11:28"/>
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a>  <a href="group_4.html#K5">gr</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c</font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i>, <a class="ref" href="gr_cy_2.html#T11">GR_CY_2:11</a></i>;<br/>
<b>hence </b><a NAME="E12:28"/>
<font color="Maroon">H</font> is  <a href="gr_cy_1.html#V1">cyclic</a> <a href="group_1.html#NM1">Group</a>
 <b>by </b><i><a class="ref" href="gr_cy_2.html#T10">GR_CY_2:10</a></i>;<br/>


</div>
